The pair believe Australia is on the American path to deep division unless Rupert Murdoch's hyper-partisan media operations are kept in check.
Petitions committee chair Ken O'Dowd was impressed with the number of Australians engaging with parliament and democracy.
Mr O'Dowd told parliament on Monday the top paper petitions in Australian history related to community pharmacies and beer prices.
Mr Turnbull, a former Liberal prime minister, said the Murdoch media used to be a group of traditional right-leaning outlets but has now become "a vehicle of propaganda."
He told ABC television's Insiders program on Sunday that Australian democracy was suffering for allowing the "crazy, bitter partisanship" of social media to creep into the mainstream.
"We have to work out what price we're paying, as a society, for the hyper-partisanship of the media," Mr Turnbull said.
"Look at the United States and the terrible, divided state of affairs that they're in, exacerbated, as Kevin was saying, by Fox News and other right-wing media."
He warned that allowing the media to become increasingly partisan was dreadful for democracy because people ended up being unable to agree on shared facts to form the basis of political debate.
"We are seeing people are being able to live in a siloed echo chamber that reinforces their prejudices, that appeals to the worst demons of their nature rather than the better angels," Mr Turnbull said.
"And if you want to see an example of what that does to a country, look at the United States.
"So I reckon we've got some very big issues with the media. It has changed dramatically the whole environment."
Former Labor prime minister Kevin Rudd hopes an inquiry will recommend ways to maximise media diversity because the Murdoch media was like a monopoly.
"It's symptomatic of a broader cancer on our democracy, and my principle motivation in putting this petition together has been to bring to the surface this national conversation - rather than people being too frightened to talk about it," Mr Rudd said.
"Murdoch has engendered a culture of fear in Australia about this discussion because he goes after people individually who raise this question, including myself, including Malcolm."